非凸共轭梯度p范数正则化SVM分类算法

Classifier ofp-norm Regularizing SVM with Nonconvex Conjugate Gradient Algorithm

经典的p范数支持向量机分类算法的正则化阶次p往往被选定为0、1或2。但是通过大量的实验可知,p取0、1或2的分类效果并不一定是最佳的。针对不同的数据使用不同的正则化阶次,可以改进分类算法的预测准确率。刘建伟等从目前迭代再权的思想出发讨论了p范数正则化支持向量机问题,但由于每次求解的均是原问题的近似问题,因而得到的解是近似解。从最优化角度出发,应用非凸共轭梯度算法求解0<p<1时的p范数正则化支持向量机问题,分别对3种不同的支持向量机问题进行了求解,并通过处理3种典型的癌症数据集展示了算法的良好分类效果。

Classical classification algorithm of SVM via p norm regularization usually takes the regular-ization parameter p as 0,1 or 2. However,large amount of experiments show that these parameters can not always achieve the best classification results. It means finding out the appropriate parameter accord-ing to specific dataset may help promote the predictive rate. LIU Jian-wei has already discussed this problem. However,as it is based on the idea of reweighed iteration,it only gets the approximate solution of the original problem. The original problem was solved from the point of optimization when 0〈p〈1. Three different kinds of SVM have been discussed and the classification results are shown with the ex- periments on three gene datasets.